Mechanical state-space linearization of mechanical control systems and symmetric product of vector fields ?

摘要

We study mechanical control systems and their linearization via diffeomorphisms that preserve their mechanical structure, called mechanical state-space linearization, that is, the transformed system is linear and mechanical. We provide necessary and sufficient conditions for the mechanical linearization, verifiable in terms of the dynamics of the original system. We also give a classification of linear mechanical control systems with the help of their invariants and illustrate our results by examples.